But it was unclear whether the communist-rooted party, led by 40-year-old Alexis Tsipras, had won by a big enough margin over Prime Minister Antonis Samaras' incumbent conservatives to govern alone. For that, they need a minimum 151 of parliament's 300 seats.
Tsipras has promised to renegotiate the country's 240 billion-euro ($270 billion) international bailout deal, and seek forgiveness for most of Greece's massive debt load.
He has pledged to reverse many of the reforms that creditors demanded, including cuts in pensions and the minimum wage, some privatizations and public sector firings, in exchange for keeping Greece financially afloat since 2010.
"There is great relief among all Europeans. The only question is how big a victory it is."
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Skourletis said the election results heralded "a return of social dignity and social justice. A return to democracy. Because, beyond the wild austerity, democracy has suffered."
Syriza's anti-bailout rhetoric appealed to many in a country that, in the past five years of its acute financial crisis, has seen a quarter of its economy wiped out, unemployment of above 25 percent, and average income losses of at least 30 percent.
Samaras' New Democracy party conceded defeat not too long after the exit poll was announced.